## Encyclopedia of Physical Science and Technology, Volume 1 |

### From inside the book

Results 1-3 of 7

Page 397

Differential form: Section of a bundle of antisymmetric tensors. Geodesic: General

geometrical equivalent of a straight line in Euclidean geometry.

Fundamental tensor field for prescribing metrical geometry on a manifold.

Parallel ...

Differential form: Section of a bundle of antisymmetric tensors. Geodesic: General

geometrical equivalent of a straight line in Euclidean geometry.

**Metric tensor**:Fundamental tensor field for prescribing metrical geometry on a manifold.

Parallel ...

Page 414

B.

is, a section of T\M g: M-* T°2M :x\^>gx € TXM* ® TXM* where gx: 7xil/ x TXM -» R

: («, u) l-» &,(«, u) satisfies the conditions 1. Symmetry: gx(u, v) = gx(v, u). 2.

B.

**Metric Tensors**A**metric tensor**on an n-manifold M is an element g e T\M, thatis, a section of T\M g: M-* T°2M :x\^>gx € TXM* ® TXM* where gx: 7xil/ x TXM -» R

: («, u) l-» &,(«, u) satisfies the conditions 1. Symmetry: gx(u, v) = gx(v, u). 2.

Page 415

There is a dual

, 0) with coordinate expression £,* = (** 3, ® djh and (#«) = (*„)-' as matrices, well

defined since det g^ 4 0. 3. There is an isomorphism Y?M =« Y^M of tangent ...

There is a dual

**metric tensor**g* 6 Y/jA/ with g*: TXM* x 7"XA/* -» R : (a, /3)H- g* (a, 0) with coordinate expression £,* = (** 3, ® djh and (#«) = (*„)-' as matrices, well

defined since det g^ 4 0. 3. There is an isomorphism Y?M =« Y^M of tangent ...

### What people are saying - Write a review

#### Encyclopedia of physical science and technology

User Review - Not Available - Book VerdictAlthough almost a decade has passed since the second edition of this work was published, this encyclopedia's reputation as a high-quality scholarly work has not diminished. Guided by an advisory board ... Read full review

### Contents

Liquid Alkali Metals 1 John F Schenck | 337 |

Liquid Chromatography 13 Russell L Rasmussen Joseph | 363 |

Liquid Crystal Devices 41 Manifold Geometry | 397 |

Copyright | |

14 other sections not shown

### Other editions - View all

### Common terms and phrases

acid alkali metals alloys applications atoms axis bond brane carbon cell chain chemical column components composition compounds concentration core defined deformation density device electric electrons elements emission energy engine equation example excited ferromagnetic finite flow fluorine flux force frequency fuel function heat HPLC hydrazine hydride hydrogen integral isotactic layer liquid crystal LISP load machine magnetic field mantle masonry materials measure mechanical melting membrane ment metal methods metric tensor mobile phase molecular molecules monomer monopropellants motion nematic nitric acid nitrogen oxide oxygen particles pervaporation plastic polarization polymer pressure propellant properties protons reaction result reverse osmosis rotation sample Section separation sequence shown in Fig smectic sodium solid solution solvent space specific spin steel stress structure surface syndiotactic temperature theorem theory thermal tion ture UDMH units vector velocity viscosity voltage workpiece